Why is the symmetrize function cutting a face?
2 steps to solving this. 


Firstly, to mirror to the other side of the head, your origin point needs to be in the center of the head because the orogin is the point everything is mirror from.
Then
Immediatly after symmetrizing a menu in the lower left will appear saying "Symmetrize". Click the triangle and a drop down will appear. Change the direction until you find something that fits your intention. It appears that you want to select X+ to -X in your object transforms, but this could depend on your objects rotation because the symmetry is local to the object's rotation as apposed to constant to the world scale.